A perturbation approach for an inverse quadratic programming problem over second-order cones

doi:10.1090/s0025-5718-2014-02848-2

科研成果详情

题名	A perturbation approach for an inverse quadratic programming problem over second-order cones
作者	Zhang，Yi 1; Zhang，Liwei 2; Wu，Jia 2; Zhang，Jianzhong 3
发表日期	2015
发表期刊	Mathematics of Computation
ISSN/eISSN	0025-5718
卷号	84 期号:291 页码:209-236
摘要	This paper is devoted to studying a type of inverse second-order cone quadratic programming problems, in which the parameters in both the objective function and the constraint set of a given second-order cone quadratic programming problem need to be adjusted as little as possible so that a known feasible solution becomes optimal. This inverse problem can be written as a minimization problem with second-order cone complementarity constraints and a positive semidefinite cone constraint. Applying the duality theory, we reformulate this problem as a linear second-order cone complementarity constrained optimization problem with a semismoothly differentiable objective function, which has fewer variables than the original one. A perturbed problem is proposed with the help of the projection operator over second-order cones, whose feasible set and optimal solution set are demonstrated to be continuous and outer semicontinuous, respectively, as the parameter decreases to zero. A smoothing Newton method is constructed to solve the perturbed problem and its global convergence and local quadratic convergence rate are shown. Finally, the numerical results are reported to show the effectiveness for the smoothing Newton method to solve the inverse second-order cone quadratic programming problem.
关键词	Inverse optimization Perturbation approach Second-order cone quadratic programming Smoothing Newton method
DOI	10.1090/s0025-5718-2014-02848-2
URL	查看来源
语种	英语English
Scopus入藏号	2-s2.0-84930429778
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://repository.uic.edu.cn/handle/39GCC9TT/6468
专题	北师香港浸会大学
作者单位	1.Department of Mathematics,School of Science,East China University of Science and Technology,Shanghai,200237,China 2.School of Mathematical Sciences,Dalian University of Technology,Dalian,116024,China 3.Division of Science and Technology,Beijing Normal University-Hong Kong Baptist University United International College,Zhuhai,519085,China
推荐引用方式 GB/T 7714	Zhang，Yi,Zhang，Liwei,Wu，Jiaet al. A perturbation approach for an inverse quadratic programming problem over second-order cones[J]. Mathematics of Computation, 2015, 84(291): 209-236.
APA	Zhang，Yi, Zhang，Liwei, Wu，Jia, & Zhang，Jianzhong. (2015). A perturbation approach for an inverse quadratic programming problem over second-order cones. Mathematics of Computation, 84(291), 209-236.
MLA	Zhang，Yi,et al."A perturbation approach for an inverse quadratic programming problem over second-order cones". Mathematics of Computation 84.291(2015): 209-236.